Answer:
A) ( -5 , -2)
Centro-id of a triangle = ( -5 , -2)
Step-by-step explanation:
Given the vertices at D (0, 0), E (–8, 0), and F (–7, – 6)
Centro-id of triangle
= [tex](\frac{x_{1} + x_{2} + x_{3} }{3} ,\frac{y_{1}+y_{2} +y_{3} }{3} )[/tex]
= [tex](\frac{0-8-7 }{3} ,\frac{0+0-6 }{3} )[/tex]
= [tex](\frac{-15}{3} ,\frac{-6}{3} )[/tex]
= ( -5 , -2)
Final answer:-
Centro-id of a triangle = ( -5 , -2)
Answer:
(-5,-2)
Step-by-step explanation:
I took the exam and got the question correct :)
Use triangle ABC to write the value of tan A as a ratio.
What is the ratio for tan A
Enter your answer as a fraction in simplest form, like this: 42/53
A 160 ft. long wire has a resistance of 16.2 12. What would the resistance of 8 ft. of wire be?
Answer: Resistance = 0.8106 ohms.
Step-by-step explanation:
Electrical resistance is proportional to the length of a wire.
The relationship between resistance and length of a wire can be expressed as;
L1/R1 = L2/R2
Let L1 = 160 ft, R1 = 16.212 ohms
L2 = 8ft, R2 = ?
Substitutes all the parameters values into the formula
160/16.212 = 8/R2
Cross multiply
160R2 = 129.696
R2 = 129.696/160
R2 = 0.8106 ohms.
Therefore, the resistance of 8 ft. of wire will be 0.8106 ohms.
Find the derivatives of the function
Answer:
Part B)
[tex]\displaystyle h^\prime(t)=\frac{2t^3(4-t^3)}{(t^3+2)^3}[/tex]
Part C)
[tex]h^\prime(t)=-4\pi\cot(\pi t+2)\csc^2(\pi t+2)[/tex]
Step-by-Step Explanation:
Question B)
We have:
[tex]\displaystyle h(t)=(\frac{t^2}{t^3+2})^2[/tex]
And we want to find the derivative, h‘(t).
This will require the chain rule and the quotient rule. Remember that the chain rule states:
[tex]\displaystyle \frac{d}{dx}[(u(v(x))]=u^\prime(v(x))\cdot v^\prime(x)[/tex]
And the quotient rule:
[tex]\displaystyle \frac{d}{dx}[\frac{u}{v}]=\frac{u^\prime v-uv^\prime}{v^2}[/tex]
Therefore, for our function h(t), we can let, by the chain rule:
[tex]\displaystyle v(t)=\frac{t^2}{t^3+2}\text{ and } u(t)=t^2[/tex]
Then by the quotient rule:
[tex]\displaystyle v^\prime(t)=\frac{2t(t^3+2)-t^2(3t^2)}{(t^3+2)^2}\text{ and } u^\prime(t)=2t[/tex]
Then, by the chain rule, our derivative, h’(t), is:
[tex]\displaystyle h^\prime(t)=2(\frac{t^2}{t^3+2})(\frac{2t(t^3+2)-t^2(3t^2)}{(t^3+2)^2})[/tex]
Simplify:
[tex]\begin{aligned} \displaystyle h^\prime(t)&=2(\frac{t^2}{t^3+2})(\frac{2t(t^3+2)-t^2(3t^2)}{(t^3+2)^2})\\ \\ &=\frac{2t^2}{t^3+2}(\frac{2t^4+4t-3t^4}{(t^3+2)^2})\\ \\ &= \frac{2t^2}{t^3+2}(\frac{-t^4+4t}{(t^3+2)^2}) \\ \\ &=\frac{2t^3(4-t^3)}{(t^3+2)^3} \end{aligned}[/tex]
Part C)
We have:
[tex]h(t)=2\cot^2(\pi t+2)[/tex]
Again, we will utilize the chain rule. This time, we will let:
[tex]u(t)=x^2\text{ and } v(t)=\cot(\pi t+2)[/tex]
Then differentiating gives (on the right, we will apply the chain rule a second time):
[tex]u^\prime(t)=2t\text{ and } v^\prime(t)=-\pi\csc^2(\pi t+2)[/tex]
To differentiate v(t), as mentioned, we need to apply the chain rule. We have:
[tex]v(t)=\cot(\pi t+2)[/tex]
We will let:
[tex]u_2(t)=\cot(t)\text{ and } v_2(t)=\pi t+2[/tex]
Therefore:
[tex]u_2^\prime(t)=-\csc^2(t)\text{ and } v_2^\prime(t)=\pi[/tex]
So:
[tex]v^\prime(t)=-\csc^2(\pi t+2)(\pi)[/tex]
And by simplification:
[tex]v^\prime(t)=-\pi\csc^2(\pi t+2)[/tex]
Therefore, it follows that:
[tex]h^\prime(t)=2[2(\cot(\pi t+2))(-\pi \csc^2(\pi t+2))][/tex]
So:
[tex]h^\prime(t)=-4\pi\cot(\pi t+2)\csc^2(\pi t+2)[/tex]
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
243,729
Step-by-step explanation:
You just need to multiply each number by 3.
I hope this help you :)
Answer:
243, 729
Explanation:
To solve this problem we must first understand what the pattern is in the sequence. Once we understand the pattern, we can then apply it to the final known term to find the next two terms.
Take a look at the sequence given:
1, 3, 9, 27, 81,...
Let's start by figuring out how they got the second term in the sequence. To do that, identify what basic operation and number must be applied. This will reveal the pattern.
1 - first term
3 - second term
1 ? ? = 3
1 × 3 = 3
So, this means the sequence multiplied three to get the next term. Therefore, the pattern should be 'multiply three' to get the next term. Just to be sure the pattern we found is correct, apply it to the given sequence.
1, 3, 9, 27, 81,...
1 × 3 = 3
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
So, since 'multiply three' every time gives us the next term, the pattern is correct.
Finally, let's continue the pattern to find the next two terms.
81 × 3 = 243
243 × 3 = 729
Therefore, the next two terms in the sequence are 243, 729.
The parabola whose equation is
y = ax2 + bx + c passes through the points
(-3, -40), (0, 29), and (-1, 10). What is an
equation of the line of symmetry?
PLEASE EXPLAIN bc I really don’t understand
Answer:
29
Step-by-step explanation:
23
What percent of the rectangle below is shaded?
Answer:
80% of the rectangle is shaded.
Step-by-step explanation:
There are 10 rows and of those rows 8 are shaded.
Answer:
D
Step-by-step explanation:
80/10
10 20 30 40 50 60 70 80 90 100
8 shaded so 80 percent
Find a formula for the nth term
of the arithmetic sequence.
First term 10
Common difference -3
Answer:
For an nth term in an arithmetic sequence
U(n) = a + (n - 1 )d
a = first term
d = common difference
U(n) = 10 + (n -1)-3
= 10 - 3n + 3
= 13 - 3n
Hope this helps.
Answer: -3n + 13
Step-by-step explanation:
If P(x,y) is the point on the unit circle determined by real number 0, then tan0=
Answer: 0
Step-by-step explanation:
You can solve for tangent by dividing sin by cos.
Looking at the unit circle, at 0, sin is 1 and cos is 0, so you would simply have 0/1, which equals zero.
Answer:
y/x. Just took a quiz and this was the answer
Helpppppppp??????????
Answer:
Answer is option d
Answer is given below with explanations.
Step-by-step explanation:
We can prove that the two triangles are similar.
We can prove this using AA criterion of similarity.
In triangle DNC and triangle QSC
Vertically opposite angles are equal.
Then Angle QCS = Angle DCN
Two parallel lines cut by a transversal line make the alternate angles are equal.
Then Angle NDC = Angle CQS
By AA criterion of similarity
TRIANGLE DNC ~ TRIANGLE QSC
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Point S is located at(9,−3). Point T is located at (4,-3)
Answer:
if 52x=1 what is the value of x
Answer:
5.
Step-by-step explanation:
Khan academy (I tried 5 and it was correct)
A triangle has vertices A (-5, -4), B (2, 6), and C (4, -3). The center of dilation is the origin and (x, y) changes to (3x, 3y). What are the vertices of the dilated image?
Answer:
(-15,12),(6,18)(12,-9)
Step-by-step explanation:
Given
A (-5, -4), B (2, 6), and C (4, -3)
Dilated from (x,y) to (3x,3y)
Required
Vertices of the dilated image
First, the scale factor has to be calculated
This is calculated as thus;
Dilation = Original * Scale Factor;
In case of (x,y) to (3x,3y)
So, we have
[tex](3x,3y) = Scale\ Factor * (x,y)[/tex]
Simplify brackets
[tex]3(x,y) = Scale\ Factor * (x,y)[/tex]
Divide both sides by (x,y)
[tex]\frac{3(x,y)}{(x,y)} = \frac{Scale\ Factor * (x,y)}{(x,y)}[/tex]
[tex]\frac{Scale\ Factor * (x,y)}{(x,y)}=\frac{3(x,y)}{(x,y)}[/tex]
[tex]Scale\ Factor =\frac{3(x,y)}{(x,y)}[/tex]
[tex]Scale\ Factor =3[/tex]
Now, the vertices of the new image can be calculated;
Using the formula: Dilation = Original * Scale Factor;
At vertex A(-5,4)
Dilation = (-5,4) * 3
Dilation = (-5*3 ,4*3)
Dilation = (-15,12)
At vertex B(2,6)
Dilation = (2,6) * 3
Dilation = (2*3 ,6*3)
Dilation = (6,18)
At vertex C(4,-3)
Dilation = (4,-3) * 3
Dilation = (4*3 ,-3*3)
Dilation = (12,-9)
Hence, the vertices of the dilated image are (-15,12),(6,18)(12,-9)
Simplify the following expression. (x^0*y^2/3*z−2)^3/2 / (x^2*z^1/2)^−6
Answer:
x^12 * z^3 (zy^2/3 - 2) ^3/2
x to the power of 12 times z cubed (zy to the power of two thirds minus 2) exponent three halves
Step-by-step explanation:
Please help
i need ASAP
Answer:
6 and 6
Step-by-step explanation:
In equilateral triangles, all sides are congruent so that means that BC and CA are both 6.
Answer:
BC = 6
CA = 6
Step-by-step explanation:
In an equilateral triangle all measures of side are equal.
Therefore,
AB = BC = CA = 6
What is the solution set of the equation x+3x+2=3+1x? Note: x≠0, −2 {−1, 1} {2} {−1, 2} {−1}
Answer:
Interpreting as: x+3x+2=3+1x
Input:
x + 3 x + 2 = 3 + 1 x
Result:
4 x + 2 = x + 3
We want to find the solution set of the equation:
x + 3x + 2 = 3 + 1/x
The solution set is { (1 + √17)/8, (1 - √17)/8)}
To find this, we just need to solve the equation for x.
We start with:
x + 3x + 2 = 3 + 1/x
We simplify this to:
(x + 3x) + 2 = 3 + 1/x
4x + 2 = 3 + 1/x
4x + 2 - 3 - 1/x = 0
4x - 1 - 1/x = 0
Then we multiply by x in both sides to get:
4x^2 - x - 1 = 0
This is just a quadratic equation, the solutions are given by Bhaskara's equation.
[tex]x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*4*(-1)} }{2*4} \\\\x = \frac{1 \pm \sqrt{17} }{8}[/tex]
Then the solution set is: { (1 + √17)/8, (1 - √17)/8)}
If you want to learn more, you can read:
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HELP! WILL GIVE BRAINLIEST! Given the table of values below which of the following ordered pairs are found on the graph of the inverse function?
Answer:
C. (2,-2), (7,-1), (12,0), (17, 1), (22,2)
Step-by-step explanation:
a p e x , just took the quiz
can you divide by zero
Answer:
No
Step-by-step explanation:
When you divide by 0, you will get an undefined error. When you try to graph a divide by 0, you will get asymptotes.
Answer:
no
Step-by-step explanation:
What is the solution to -2(8x - 4) < 2x + 5?
O x>
O x<
X>6
x < 6
Answer:
1/6 <x
Step-by-step explanation:
-2(8x - 4) < 2x + 5
Distribute
-16x +8 < 2x+5
Add 16x to each side
-16x+16x +8 < 2x+16x+5
8 < 18x +5
Subtract 5 from each side
8-5 <18x
3 <18x
Divide by 18
3/18 <x
1/6 <x
-2(8x - 4) < 2x + 5
Expand the brackets.
-16x +8 < 2x + 5
Add -2x and -8 on both sides.
-16x -2x<5-8
-18x<-3
Multiply both sides with -1 (reverse the inequalty).
18x>3
Divide 18 into both sides.
18x/18>3/18
x>1/6Which of these systems of linear equations has no solution? A. 2 x + 8 y = 15. 4 x + 16 y = 30. 2 x minus B. y = 18. 4 x + 2 y = 38. C. 4 x + 7 y = 17. 8 x minus 14 y = 36. D. 4 x minus 3 y = 16. 8 x minus 6 y = 34.
Answer:
D. 4 x minus 3 y = 16. 8 x minus 6 y = 34
Step-by-step explanation:
A. 2 x + 8 y = 15. 4 x + 16 y = 30.
Multiply the first equation by 2
4x+16y = 30 This is identical to the second equation so there are infinite solutions
B. 2 x - y = 18. 4 x + 2 y = 38.
Multiply the first equation by 2
4x -2y = 36. Add to the second equation 8x = 74 so there is one solution
C. 4 x + 7 y = 17. 8 x minus 14 y = 36.
Multiply the first equation by 2
8x +14y = 34 Add this to the second equation 16x = 70 There is one solution
D. 4 x minus 3 y = 16. 8 x minus 6 y = 34.
Multiply the first equation by 2
8x - 6y = 32 Subtract this from the second equation 8x - 6y = 34
0 = 2
This is never true so there is no solution
Answer:
d
Step-by-step explanation:
hi:) I tried using the sine rule but I couldn’t get the ans :( anyone able to help? Thank you:)!!
Answer:
141.9° (1 d.p.)
Step-by-step explanation:
Please see attached picture for full solution.
Sine rule cannot be used since there is no given angle in △PQR. Note that the bearing of Q from P (041°) equals to ∠NPQ not ∠PQR.
Help please.The length of a rectangle is 2 times the width. If the perimeter is to be less than 108 meters. What are the possible values for the width.
If the only perimeters are that the length has to be twice the width and less than 108 meters then there are an infinite amount of possible values for width. For example: 1.0002 and 2.0004 or 4 and 8. You can use an infinite amount of decimal places and therefore have an infinite amount of values.
The largest the width can be is the limit approaching 18 and it has to be greater than 0 tho
PLS HELP How many cubes with side lengths 1/4 of does it take to fill the prism
1 whole or 4/4 time's what its being compaired to then multiply to get your answer! :D stay safe!
Answer:
224
Step-by-step explanation:
Khan hehe
If 3* = 54, then which of the following must be true?
Answer: 3 < pi < 4
Step-by-step explanation:
6,000 = bu + 4,000. Given the above equation with constant b, what is the value of 600,000 + 100 bu + 400,000 in millions?
Answer:
1.2 million
Step-by-step explanation:
First multiply the equation by 100. You get:
600,000 = 100bu + 400,000
Now recognize that you can substitute:
600,000 + 100bu + 400,000
= 600,000 + (600,000)
= 1,200,000
That’s 1.2 million.
The value of the equation given is 1.2 millions.
What are equations?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that, an equation, 6,000 = bu + 4,000, we need to find the value of the equation 600,000 + 100 bu + 400,000,
So, In the equation 1, multiply by 100, we get,
6,000 = bu + 4,000
600000 = 100 bu + 400000
Now, put this in equation 2,
600,000 + 100 bu + 400,000
= 600000 + 600000
= 1200000
= 1.2 millions
Hence, the value of the equation given is 1.2 millions.
Learn more about equations, click;
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Jason’s budget is shown in the circle graph below. His total monthly budget is $3,000. How much does Jason spend on groceries?
A $25
B $150
C $450
D $750
Answer:
D.) 750
Step-by-step explanation:
3000-25%= 2250
3000-2250=750
Answer:
(D) $750
Step-by-step explanation:
[tex]3000* 0.25=750[/tex]
What is 7/8 divided by 1/4
Answer:
7/2
Step-by-step explanation:
you got two fractions you wanna divide flip the right and multiply
7/8 times 4/1 = 7/2
7/8 divided by 1/4 is equal to 7/2.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have:
(7/8) ÷ (1/4)
To find the reciprocal of 1/4, we flip the fraction, which gives us 4/1.
Now, we can multiply the first fraction by the reciprocal:
(7/8) × (4/1)
Multiplying the numerators and denominators, we get:
(7 × 4) / (8 × 1)
28/8
The fraction 28/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:
(28 ÷ 4) / (8 ÷ 4)
7/2
Therefore, 7/8 divided by 1/4 is equal to 7/2.
To learn more about the division;
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Edmund makes a cube using eight small cubes.
Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund’s cube
Answer: 184
Step-by-step explanation:
so edmund would have a 2 by 2 cube (try and draw it out if that helps) so
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
so samuel cubeboid would be
long = 4
wide = 6
hight = 8
8 x 6 x 4 = 192 small cubes
but we are trying to find how much more samuel got
so 192 - 8 = 184
In ΔCDE, m∠C = (9x+11)^{\circ}(9x+11) ∘ , m∠D = (3x-15)^{\circ}(3x−15) ∘ , and m∠E = (2x+16)^{\circ}(2x+16) ∘ . What is the value of x?
Answer:
x = 12
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180, that is
9x + 11 + 3x - 15 + 2x + 16 = 180, simplify left side
14x + 12 = 180 ( subtract 12 from both sides )
14x = 168 ( divide both sides by 14 )
x = 12
The value of a car decreases $500 for every 1,000 miles it is driven. The current value of the car is $23,000, and the car is driven an average of 10,000 miles per year. What will be the value of the car, in dollars, at a point in time y years from now?
A) $23,000 − $500y
B) $23,000 − $0.02y
C) $23,000 − $5,000y
D) $23,000 − $0.0002y
Answer: C
Step-by-step explanation:
If we know the value of the car decreases $500 for every 1,000 miles, and that the car is driven about 10,000 miles every year, that means that you need to take the total value of the car (23,000) and subtract it from the amount of money it is losing per year. Again, the car is driven about 10,000 miles per year, so that means that the car will most likely continue to be driven 10,000 miles per year. If you do the math, for one year, the value of the car will drop $5,000 ($500 x 10, because it is $500 per every 1,000 miles) So, for each year, you can just multiply the number of years by $5,000 to find out how much the vehicle has depreciated over time.
Hope this helped you and made sense! Feel free to ask me any questions you have!
y=-2
x=-2y=6
y=-2
x+2y=6
x=-2
2x-y=3
x=-2
2x+y=-3
Answer:x+y=24
is the respuesta
Which of the following are solutions to lx-1|=5x+2? Check all that apply
Answer:
x=-3/4 x=-1/4
Step-by-step explanation:
x-1=5x+2
-3=4x
x=-3/4
x+1=5x+2
-1=4x
x=-1/4